*** UPDATE ***
Most new GoDaddy accounts now do support standard PHP mail and/or PHP mailer, so that means you can use the built-in form script.
The following information may no longer be valid.

*** START OF OLD FAQ ***
Unfortunately some hosting accounts on godaddy hosting do not support phpmail.
This means that you cannot use the built-in form processor, because it relies on phpmail to send emails.
However you can still use forms created in WYSIWYG Web Builder with godaddy! But instead of using the built-in form processor you will need to use godaddy's own form processor.

Step 1:
Create your form as usual, but do not enable 'use built-in php form processor'!

Step 2:
In the action property of the form enter:/gdform.php

Step 3:
Make the encoding type property empty.

Step 4:
In 'Hidden fields' add the following fields:
Name: subject
Value: Form Submission
(where 'Form Submission' is the name of the subject)

Name: redirect
Value: thankyou.html
(where 'thankyou.html' is the name of the 'Thank you' page.